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The article discusses the Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) satellite mission, which is a joint effort between the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). The mission aims to improve weather forecasts and climate projections by studying cloud, aerosol, and radiation processes. EarthCARE will use novel instruments to retrieve more accurate properties of clouds, aerosols, and precipitation, and provide in-orbit verification of their impact on radiative fluxes. The article also pays tribute to Dr. Tobias Wehr, the mission scientist who passed away in 2023 and played a crucial role in the development of EarthCARE. [Extracted from the article]

The race for the most efficient, accurate, and universal algorithm in scientific computing drives innovation. At the same time, this healthy competition is only beneficial if the research output is actually comparable to prior results. Fairly comparing algorithms can be a complex endeavor, as the implementation, configuration, compute environment, and test problems need to be well‐defined. Due to the increase in computer‐based experiments, new infrastructure for facilitating the exchange and comparison of new algorithms is also needed. To this end, we propose a benchmark framework as a set of generic specifications for comparing implementations of algorithms using test cases native to a community. Its value lies in its ability to fairly compare and validate existing methods for new applications, as well as compare newly developed methods with existing ones. As a prototype for a more general framework, we have begun building a benchmark tool for the model order reduction (MOR) community. The data basis of the tool is the collection of the Model Order Reduction Wiki (MORWiki). The wiki features three main categories: benchmarks, methods, and software. An editorial board curates submissions and patrols edited entries. Data sets for linear and parametric‐linear models are already well represented in the existing collection. Data sets for non‐linear or procedural models, for which only evaluation data, or codes/algorithmic descriptions, rather than equations, are available, are being added and extended. Properties and interesting characteristics used for benchmark selection and later assessments are recorded in the model metadata. Our tool, the Model Order Reduction Benchmarker (MORB), is under active development for linear time‐invariant systems and solvers. An ontology (MORBO) and knowledge graph are being developed in parallel. They catalog benchmark problem sets and their metadata and will also be integrated into the Mathematical Research Data Initiative (MaRDI) Portal to help improve the findability of such data sets. MORB faces a number of technical and field‐specific challenges, and we hope to recruit community input and feedback while presenting some initial results. [ABSTRACT FROM AUTHOR]

The augmented Lagrangian method (ALM) is classic for canonical convex programming problems with linear constraints, and it finds many applications in various scientific computing areas. A major advantage of the ALM is that the step for updating the dual variable can be further relaxed with a step size in (0,2), and this advantage can easily lead to numerical acceleration for the ALM. When a separable convex programming problem is discussed and a corresponding splitting version of the classic ALM is considered, convergence may not be guaranteed and thus it is seemingly impossible that a step size in (0,2) can be carried on to the relaxation step for updating the dual variable. We show that for a parallel splitting version of the ALM, a step size in (0,2) can be maintained for further relaxing both the primal and dual variables if the relaxation step is simply corrected by a rank-two matrix. Hence, a rank-two relaxed parallel splitting version of the ALM with a step size in (0,2) is proposed for separable convex programming problems. We validate that the new algorithm can numerically outperform existing algorithms of the same kind significantly by testing some applications. [ABSTRACT FROM AUTHOR]

It is particularly important to plan and design the rural landscape of the Qiang nationality, but the regional characteristics of the rural landscape of the Qiang nationality in the upper reaches of the Minjiang River must be maintained at the same time. On the basis of the regional culture formed by the regional geography and cultural environment of the Qiang ethnic group in the upper reaches of the Minjiang River, combined with the investigation of the Qiang ethnic group in the upper reaches of the Minjiang River, this study explores the formal characteristics and formation reasons of the rural landscape of the Qiang ethnic group in the upper reaches of the Minjiang River from the perspective of rural landscape planning and design. It summarizes the formal features of the Qiang rural landscape in the upper reaches of the Minjiang River in a graphical language. It analyzes the problems faced by traditional rural landscapes. It then summarizes the experience and deficiencies in practice through the research on the existing Qiang rural landscape planning and design. It analyzes the influence of the regional culture of the Qiang nationality on the planning and design of the rural landscape of the Qiang nationality and proposes a strategy for the planning and design of the rural landscape of the Qiang nationality. This study hopes that this can provide theoretical and practical reference for the planning and design methods of the Qiang rural landscape in the upper reaches of the Minjiang River and the protection, development, and dissemination of the Qiang culture in the upper reaches of the Minjiang River. Experiments show that there are 764 settlements when the radius of the river buffer is within 500 meters. [ABSTRACT FROM AUTHOR]

In the current era of increasingly complex social life, as people's demand quality is getting higher and higher, the solution of the problem often has multiple indicators to achieve the optimum. This forces the graph coloring problem (GCP) to become complicated, and it is difficult to directly obtain the optimal solution, which brings new challenges to the solution of the problem. In response to this problem, the GCP field is of great research significance. With the in-depth study of GCP, the research on multiobjective optimization (MOO) in graph coloring algorithm (GCA) is gradually carried out. Its performance advantage is of great significance for solving multicondition constraint problems. This paper aims to study the application of Genetic Algorithm (GA) in GCA. Through the analysis and research of GA, and the fusion of numerical analysis and scientific computing, it can be applied to the construction of the neighbor distinguishable uniform V-full coloring algorithm (AVDEVTCA) to solve the AVDEVTC problem. This paper describes the basic theory of MOO and graph coloring. It conducts an experimental analysis of the algorithm performance and uses the relevant theoretical formulas to explain it. The results show that the algorithm takes 5754.142 S seconds to test 21325415 images and can color a large number of results that cannot be done manually in less time. It has greatly improved in terms of time and manpower saving and greatly improved practicability and work efficiency. [ABSTRACT FROM AUTHOR]

Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive categorization of block Gram-Schmidt algorithms, particularly those used in Krylov subspace methods to build orthonormal bases one block vector at a time. Known stability results are assembled, and new results are summarized or conjectured for important communication-reducing variants. Additionally, new block versions of low-synchronization variants are derived, and their efficacy and stability are demonstrated for a wide range of challenging examples. Numerical examples are computed with a versatile Matlab package hosted at https://github.com/katlund/BlockStab , and scripts for reproducing all results in the paper are provided. Block Gram-Schmidt implementations in popular software packages are discussed, along with a number of open problems. An appendix containing all algorithms type-set in a uniform fashion is provided. [ABSTRACT FROM AUTHOR]

Distributed-memory graph algorithms are fundamental enablers in scientific computing and analytics workflows. A majority of graph algorithms rely on the graph neighborhood communication pattern, i.e., repeated asynchronous communication between a vertex and its neighbors in the graph. The pattern is adversarial for communication software and hardware due to high message injection rates and input-dependent, many-to-one traffic with variable destinations and volumes. We present benchmarks and performance analysis of graph neighborhood communication on modern large-scale network interconnects from four supercomputers: ALCF Theta, NERSC Cori, OLCF Summit and R-CCS Fugaku. Our benchmarks characterize communication from the perspectives of latency and throughput. Benchmark parameters make it possible to mimic the behaviors of complex applications on real world or synthetic graphs by varying work distribution, remote edges, message volume, and per-vertex work. We find that minor changes in the input graph can substantially increase latencies; and contention can develop in memory caches and network stacks before contention in the network itself. Further, latencies and contention vary significantly for different graph neighborhoods, motivating the need for exploring asynchronous algorithms in greater detail. When adding work, load imbalance on real-world graphs can be pronounced: latencies for the 99th percentile were 8–128× than the corresponding average latencies. Our results help analysts and developers understand the performance implications of this important pattern, especially for the impending exascale platforms. [ABSTRACT FROM AUTHOR]

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence of stable neural networks (NNs). We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities; however, there does not exist any algorithm, even randomized, that can train (or compute) such a NN. For any positive integers K > 2 and L, there are cases where simultaneously 1) no randomized training algorithm can compute a NN correct to K digits with probability greater than 1/2; 2) there exists a deterministic training algorithm that computes a NN with K − 1 correct digits, but any such (even randomized) algorithm needs arbitrarily many training data; and 3) there exists a deterministic training algorithm that computes a NN with K − 2 correct digits using no more than L training samples. These results imply a classification theory describing conditions under which (stable) NNs with a given accuracy can be computed by an algorithm. We begin this theory by establishing sufficient conditions for the existence of algorithms that compute stable NNs in inverse problems. We introduce fast iterative restarted networks (FIRENETs), which we both prove and numerically verify are stable. Moreover, we prove that only O(| log(ϵ)|) layers are needed for an -accurate solution to the inverse problem. [ABSTRACT FROM AUTHOR]

The classification inaccuracy occurs to the evaluation calculation of the total factor production impact in the traditional digital economy development area. This paper applies the fuzzy hierarchical (Visualization in Scientific Computing, VISC) algorithm to the calculation method of the total factor production impact evaluation in the digital economy development area. The quantitative recursive method is used to evaluate the ability of the data information model, to achieve the ability of controlling the acquisition of characteristic resources, and complete the classification and summary of the index parameters of the total factor production impact of the digital economy development area. Finally, the experiment proves that this calculation method is used to develop the evaluation of the impact of total factor production digital economy development area and improve the information integration and analysis capabilities, the accuracy of the evaluation of the impact of total factor production, and the efficiency of the use of digital economy development resources. [ABSTRACT FROM AUTHOR]

Fortran is still widely used in scientific computing, and a very large corpus of legacy as well as new code is written in FORTRAN 77. In general this code is not type safe, so that incorrect programs can compile without errors. In this paper, we present a formal approach to ensure type safety of legacy Fortran code through automated program transformation. The objective of this work is to reduce programming errors by guaranteeing type safety. We present the first rigorous analysis of the type safety of FORTRAN 77 and the novel program transformation and type checking algorithms required to convert FORTRAN 77 subroutines and functions into pure, side-effect free subroutines and functions in Fortran 90. We have implemented these algorithms in a source-to-source compiler which type checks and automatically transforms the legacy code. We show that the resulting code is type safe and that the pure, side-effect free and referentially transparent subroutines can readily be offloaded to accelerators. [ABSTRACT FROM AUTHOR]

• Propose the aligned storage formats ACSR and AELL. • Put forward a parallel SpMV algorithm based on ACSR and AELL formats. • Theoretically analyze the performance of SpMV on ARM processors. • Evaluate the performance of our optimization on Kunpeng 920 processors. Sparse matrix-vector multiplication (SpMV) has always been a hot topic of research for scientific computing and big data processing, but the sparsity and discontinuity of the nonzero elements in a sparse matrix lead to the memory bottleneck of SpMV. In this paper, we propose aligned CSR (ACSR) and aligned ELL (AELL) formats and a parallel SpMV algorithm to utilize NEON SIMD registers on ARM processors. We analyze the impact of SIMD instruction latency, cache access, and cache misses on SpMV with different formats. In the experiments, our SpMV algorithm based on ACSR achieves 1.18x and 1.56x speedup over SpMV based on CSR and SpMV in PETSc, respectively, and AELL achieves 1.21x speedup over ELL. The deviations between the theoretical results and experimental results in the instruction latency and cache access are 10.26% and 10.51% in ACSR and 5.68% and 2.91% in AELL, respectively. [ABSTRACT FROM AUTHOR]

SpMV (Sparse matrix-vector multiplication) is an essential component in scientific computing and has attracted the attention of researchers in related fields at home and abroad. With the continuous expansion of matrix data, the efficient parallel SpMV algorithm has become a research hotspot for research experts in related fields. The sparse matrix compression format as a critical point to improve computing performance can effectively save storage space and efficiently cooperate with the advantages of the processor system structure to give full play to performance. This paper proposes a new sparse matrix storage format CSR2 (Compressed Sparse Row 2). It is a new single format and suitable for processor platforms with SIMD (Single Instruction Multiple Data) vectorizations. The format operation of CSR2 is easy to implement with a low overhead of conversion. We compared the SpMV algorithm based on CSR2 with the most advanced single format CSR5 (Compressed Sparse Row 5) and Intel MKL (Intel Math Kernel Library) on the mainstream high-performance processor Intel Xeon E5-2670 v3 CPU. We choose 48 sets of matrices to be used as a benchmark suite. Experimental results show that CSR2 has a remarkable performance improvement compared with CSR5 and MKL. Compared to CSR5, CSR2 can achieve an average acceleration of 1.401 × (up to 1.861 ×). Compared to MKL, CSR2 can achieve an average acceleration of 1.261 × (up to 5.921 ×). In reality, for applications with multiple iterations, using our CSR2 can bring low-overhead format conversion and high-throughput computing performance. [ABSTRACT FROM AUTHOR]

Least squares form one of the most prominent classes of optimization problems with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must account for nonlinear dynamics by incorporating constraints. In addition, these systems often incorporate a large number of variables, which increases the difficulty of the problem and motivates the need for efficient algorithms amenable to large-scale implementations. In this paper, we propose and analyze a Levenberg--Marquardt algorithm for nonlinear least squares subject to nonlinear equality constraints. Our algorithm is based on inexact solves of linear least-squares problems that only require Jacobian-vector products. Global convergence is guaranteed by the combination of a composite step approach and a nonmonotone step acceptance rule. We illustrate the performance of our method on several test cases from data assimilation and inverse problems; our algorithm is able to reach the vicinity of a solution from an arbitrary starting point and can outperform the most natural alternatives for these classes of problems. [ABSTRACT FROM AUTHOR]

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this work, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems. [ABSTRACT FROM AUTHOR]

Computing reachability probabilities is a fundamental problem in the analysis of randomized programs. This article aims at a comprehensive and comparative account of various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existingworks that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points--a classic topic in computer science--in the analysis of randomized programs. This leads us to two new martingale-based techniques, too. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales. [ABSTRACT FROM AUTHOR]

Aiming at the problems of slow convergence speed, easy to fall into local optimum and low solution quality of carnivorous plant algorithm (CPA) in the existing literature, a carnivorous plant algorithm with Lévy mutation and similarity-removal operation (CPA-LMSR) is proposed. In the grouping stage, a method of grouping according to the biological species, carnivorous plants and prey, is proposed to enhance the randomness of sampling. In the growth stage, the adaptive variation of attraction rate and growth rate parameters are given. An attraction term is added to the growth model of carnivorous plants and prey, which improves the probability of generating potential offspring. During the reproduction phase, all carnivorous plants are allowed to reproduce, ensuring excellent individual information to be retained with greater probability. A similarity-removal operation and Lévy mutation operator are added to improve the exploration ability of the algorithm to maintain the diversity of the population. Finally, CPA-LMSR is tested on 28 constrained optimization problems (COPs) in CEC 2017 and two practical engineering optimization problems, and compared with seven comparison algorithms in the literature. The experimental results show that CPA-LMSR has better solution quality, stability and convergence speed than other algorithms, and the performance of various algorithms is significantly different, which is proved that CPA-LMSR can effectively solve complex constrained optimization models and provide efficient computing power for scientific decision-making in various fields of science, engineering and economy, so as to solve optimization problems in various fields. [ABSTRACT FROM AUTHOR]